Seed and thinly slice the peppers. Heat 2-3 TB olive oil over medium-high. Saute garlic until aromatic and soft. Add peppers and saute until they are soft, about 10 minutes. Add sugar and saute for a couple more minutes. Last, stir in basil for a minute. Season to taste with salt and black pepper. This pepper mixture can be made an hour or two ahead of time and set aside to warm later.
Heat oven to 375F. Slice baguette evenly into 1/2 inch thick slices. Brush each slice with olive oil on top. Place in a large pan lined with parchment paper (important for even toasting and to avoid burnt bottoms). Toast just until lightly browned, about 8-9 minutes.
Spoon pepper mixture on each baguette slice. Top with crumbled cheese. Return to oven for another minute just to warm up. Serve warm. Enjoy!